Рекурентний метод найменших квадратів: оцінювання змінних параметрів

• Видавець: The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"
• Дата: 2021
• Автор: Spectorsky, Igor
• Формат: Стаття
• Мова: Ukrainian
• Опубліковано: The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2021
• Теми: рекурентний метод найменших квадратів; РМНК; оцінювання; рекуррентный метод наименьших квадратов; оценивание; recursive less square methods; RLS; estimating
• Онлайн доступ: http://journal.iasa.kpi.ua/article/view/237815

In this paper, linear object yt=a1y1+...anyn+b1u1+...bmym+δ is considered. The aim is to estimate the object parameters with an assumption that they are changing linearly: ai=ai,0+ai,1t (i=1,2,...,n), bj=bj,0+bj,1t (j=1,2,...,m), δ=δ0+δ1t, parameters ai,0, ai,1 (i=1,2,...,n), bj,0, bj,1 (j=1,2,...,m), δ0, δ1 are assumed to be constants (almost constants during long time). For this object, the recursive least square (RLS) method is generalized. Provided examples show that the obtained RLS generalization gives higher precision (in comparison with the classical RLS method) for a case when parameters change with constant (almost constant) speed during long time. When parameters change unpredictably, the precision of the proposed RLS generalization is worse then the precision of the classical method, but it is still high.